State-of-the-art end-to-end approaches for TSP use Graph Neural Networks [1]} and sequence-to-sequence learning [2]} to construct approximate solutions directly from problem instances.
Architectures for TSP can be classified as: (1) autoregressive approaches, which build solutions in a step-by-step fashion [3]}, [4]}, [5]}, [6]}; and
(2) non-autoregressive models, which produce the solution in one shot [7]}, [8]}, [9]}.
Models can be trained to imitate optimal solvers via supervised learning or by minimizing the length of TSP tours via reinforcement learning [10]}.
Beyond TSP, other classical problems tackled by similar architectures include Vehicle Routing [11]}, [12]}, Maximum Cut [3]}, Minimum Vertex Cover [14]}, Boolean Satisfiability [15]}, [16]}, and Graph Coloring [17]}.
